Hydrogeological Models of Water Flow and Pollutant Transport in Karstic and Fractured Reservoirs. Issue 8 (29th July 2021) - Masciopinto, Costantino; Passarella, Giuseppe; Caputo, Maria C.; Masciale, Rita; De Carlo, Lorenzo
Abstract: In a literature review of the recent advancements in mathematical hydrologic models applied in fractured karstic formations, we highlight the necessary improvements in the fluid dynamic equations that are commonly applied to the flow in a discrete fracture network (DFN) via channel network models. Fluid flow and pollutant transport modeling in karst aquifers should consider the simultaneous occurrence of laminar, nonlaminar, and turbulent fluxes in the fractures rather than the laminar flow by the cubic law that has been widely applied in the scientific literature. Some simulations show overestimations up to 75% of the groundwater velocity when non‐laminar flows are neglected. Moreover, further model development is needed to address the issues of tortuosity of preferential saturated fluid flow in fractures suggesting adjustments of the size of the mean aperture in DFN models. During the past decade, DFN mathematical models have been significantly developed aimed at relating the three‐dimensional structure of interconnected fractures within rocky systems to the specific fracture properties measurable on the rock outcrops with the use of reliefs, tracer/pumping tests, and geotechnical field surveys. The capabilities and limitations of previous reported hydrological models together with specific research advancements and findings in modeling equations are described herein. New software is needed for creating three‐dimensional contour maps in fractured aquifers corresponding to the outputs of particle tracking simulations. Existing software based on the equivalent continuum or multiple‐interacting continua cannot delineate the spread of pollutant migrations affected by the tortuous preferential flow pathways that occur in DFNs. Plain Language Summary: Reading articles on mathematical models to simulate groundwater flow near karst springs or in fractured aquifers can help one realize the complexity of the mathematical equations and the importance of the data needed to obtain valid model results. This is because model results can be suitable to answer questions, such as "can the groundwater in a 300 m deep cave be contaminated by a wastewater surface runoff located 1 km upstream? If so, how long will the contamination persist? What will be the level of water contamination? Would the water still be drinkable in the future?" This paper first presents the investigation and classification of the equations that explain how these mathematical models work. We highlight the capabilities and limitations of known mathematical models and discuss ways to improve their performance (i.e., prediction accuracy) using more appropriate equations. We also show how to verify the results obtained from the models, using accurate input data from field tracer tests and geophysical measurements. Finally, some theoretical hints are used to explain how we can estimate the maximum reliability of the results of an excellent mathematical model, namely the "uncertainty" of the answers to the questions mentioned above. Key Points: Proposed velocity and tortuosity equations simulate the simultaneous occurrence of laminar and turbulent fluxes in three‐dimensional fracture networks This study provides a meaningful overview of modeling approaches used to study the flow and transport in discrete fracture networks Equivalent continuum models cannot predict the spatial distributions of tortuous pollutant paths in groundwater and channeling effects